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Jan
22
awarded  Nice Question
Jan
14
answered Formulae for Catalan's constant.
Jan
13
awarded  Nice Question
Jan
12
accepted An asymptotic behavior of $\operatorname{Li}_{-n}(a)$ for $n\to\infty$
Jan
12
awarded  Nice Question
Jan
11
answered Another beautiful arctan integral $\int_{1/2}^1 \frac{\arctan\left(\frac{1-x^2}{7 x^2+10x+7}\right)}{1-x^2} \, dx$
Jan
11
awarded  Good Answer
Jan
10
awarded  Nice Question
Jan
10
comment Conjecture ${\large\int}_0^\infty\left[\frac1{x^4}-\frac1{2x^3}+\frac1{12\,x^2}-\frac1{\left(e^x-1\right)x^3}\right]dx=\frac{\zeta(3)}{8\pi^2}$
Thanks, I fixed a typo. Could you provide some reference about this use of the Laplace transform? I'm only familiar with its application to certain differential equations.
Jan
10
revised Conjecture ${\large\int}_0^\infty\left[\frac1{x^4}-\frac1{2x^3}+\frac1{12\,x^2}-\frac1{\left(e^x-1\right)x^3}\right]dx=\frac{\zeta(3)}{8\pi^2}$
added 82 characters in body
Jan
10
asked Conjecture ${\large\int}_0^\infty\left[\frac1{x^4}-\frac1{2x^3}+\frac1{12\,x^2}-\frac1{\left(e^x-1\right)x^3}\right]dx=\frac{\zeta(3)}{8\pi^2}$
Jan
10
comment Need help with $\int_0^\infty\arctan\left(e^{-x}\right)\,\arctan\left(e^{-2x}\right)\,dx$
I wonder if the antiderivative could be simplified. I feel that possibly the number of polylogarithm terms and complex numbers can be reduced if we put to work $\operatorname{Cl}_n(z)$ and $\operatorname{Ti}_n(z)$. Unfortunately, Mathematica does not have native support for these functions.
Jan
10
revised Need help with $\int_0^\infty\arctan\left(e^{-x}\right)\,\arctan\left(e^{-2x}\right)\,dx$
edited body
Jan
10
comment Need help with $\int_0^\infty\arctan\left(e^{-x}\right)\,\arctan\left(e^{-2x}\right)\,dx$
@ClaudeLeibovici Unfortunately, inverse symbolic calculators are not perfect. See the closed form in my answer below.
Jan
10
answered Need help with $\int_0^\infty\arctan\left(e^{-x}\right)\,\arctan\left(e^{-2x}\right)\,dx$
Jan
7
awarded  Nice Question
Jan
6
answered Definite integral $\int_0^1 \frac{\arctan x}{x\,\sqrt{1-x^2}}\,\text{d}x$
Jan
6
answered What's the value of $\int_0^1\frac{1}{2y} \ln{y}\ln^2(1-y)dy$?
Jan
3
awarded  Revival
Jan
3
awarded  Excavator